Xerostomia: a common adverse effect of drugs and radiation

Reproduced with permission from Australian PrescriberThe document attached has been archived with permission from the publisher/copyright holder.Xerostomia is the subjective sensation of dry mouth. Many drugs, especially those with anticholinergic effects, can cause xerostomia, particularly in the elderly. Another major cause is radiotherapy to the head and neck damaging the salivary glands. Newer techniques to target radiotherapy and protective drugs, such as amifostine, could decrease the incidence of xerostomia.Treatment is based on either stimulating the flow of remaining salivary tissue with lollies or sialogogues such as pilocarpine, or wetting the mucosa with water or artificial saliva containing glycerine or compounds such as carboxymethylcellulose. Patients need regular dental examinations because of the effect of xerostomia on intra-oral health.Ian N Olve

A fast and spectrally convergent algorithm for rational-order fractional integral and differential equations

A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for ordinary differential equations [27], and involves constructing two different bases, one for the domain of the operator and one for the range of the operator. The bases are constructed from direct sums of suitably weighted ultraspherical or Jacobi polynomial expansions, for which explicit representations of fractional integrals and derivatives are known, and are carefully chosen so that the resulting operators are banded or almost-banded. Geometric convergence is demonstrated for numerous model problems when the variable coefficients and right-hand side are sufficiently smooth

Solution of reduced equations derived with singular perturbation methods

For singular perturbation problems in dynamical systems, various appropriate singular perturbation methods have been proposed to eliminate secular terms appearing in the naive expansion. For example, the method of multiple time scales, the normal form method, center manifold theory, the renormalization group method are well known. In this paper, it is shown that all of the solutions of the reduced equations constructed with those methods are exactly equal to sum of the most divergent secular terms appearing in the naive expansion. For the proof, a method to construct a perturbation solution which differs from the conventional one is presented, where we make use of the theory of Lie symmetry group.Comment: To be published in Phys. Rev.

Full-analytic frequency-domain 1pN-accurate gravitational wave forms from eccentric compact binaries

The article provides ready-to-use 1pN-accurate frequency-domain gravitational wave forms for eccentric nonspinning compact binaries of arbitrary mass ratio including the first post-Newtonian (1pN) point particle corrections to the far-zone gravitational wave amplitude, given in terms of tensor spherical harmonics. The averaged equations for the decay of the eccentricity and growth of radial frequency due to radiation reaction are used to provide stationary phase approximations to the frequency-domain wave forms.Comment: 28 pages, submitted to PR

Formulas for Continued Fractions. An Automated Guess and Prove Approach

We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial conditions. This is used to generate the first few coefficients and from there a conjectured formula. This formula is then proved automatically thanks to a linear recurrence satisfied by some remainder terms. Extensive experiments show that this simple approach and its straightforward generalization to difference and $q$-difference equations capture a large part of the formulas in the literature on continued fractions.Comment: Maple worksheet attache

A Necessary Condition for existence of Lie Symmetries in Quasihomogeneous Systems of Ordinary Differential Equations

Lie symmetries for ordinary differential equations are studied. In systems of ordinary differential equations, there do not always exist non-trivial Lie symmetries around equilibrium points. We present a necessary condition for existence of Lie symmetries analytic in the neighbourhood of an equilibrium point. In addition, this result can be applied to a necessary condition for existence of a Lie symmetry in quasihomogeneous systems of ordinary differential equations. With the help of our main theorem, it is proved that several systems do not possess any analytic Lie symmetries.Comment: 15 pages, no figures, AMSLaTe

Analytic structure of radiation boundary kernels for blackhole perturbations

Exact outer boundary conditions for gravitational perturbations of the Schwarzschild metric feature integral convolution between a time-domain boundary kernel and each radiative mode of the perturbation. For both axial (Regge-Wheeler) and polar (Zerilli) perturbations, we study the Laplace transform of such kernels as an analytic function of (dimensionless) Laplace frequency. We present numerical evidence indicating that each such frequency-domain boundary kernel admits a "sum-of-poles" representation. Our work has been inspired by Alpert, Greengard, and Hagstrom's analysis of nonreflecting boundary conditions for the ordinary scalar wave equation.Comment: revtex4, 14 pages, 12 figures, 3 table

Complex sine-Gordon-2: a new algorithm for multivortex solutions on the plane

We present a new vorticity-raising transformation for the second integrable complexification of the sine-Gordon equation on the plane. The new transformation is a product of four Schlesinger maps of the Painlev\'{e}-V to itself, and allows a more efficient construction of the $n$-vortex solution than the previously reported transformation comprising a product of $2n$ maps.Comment: Part of a talk given at a conference on "Nonlinear Physics. Theory and Experiment", Gallipoli (Lecce), June-July 2004. To appear in a topical issue of "Theoretical and Mathematical Physics". 7 pages, 1 figur